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We propose and demonstrate a simple method for cylindrical vector beam generation in the terahertz frequency region using optical rectification in segmented nonlinear crystals with threefold rotational symmetry. We used segmented GaP(111) plates to generate the terahertz cylindrical vector beam, and obtained clear evidence of the beam generation with a terahertz camera. By this method, a broadband terahertz cylindrical vector beam can be generated, and the radial and azimuth modes can be easily switched. We also report on the direct observation of the longitudinal electric field components at the focal point using a terahertz time-domain spectroscopy technique.
©2012 Optical Society of America
1. Introduction
Optical beams with spatially inhomogeneous polarization states have attracted great interest in recent years because of their specific properties, which offer the potential for development of new optical technologies. One of those beams is a cylindrical vector (CV) beam, which has a polarization state with axial symmetry in the beam cross section [1]. When focused with a high numerical aperture (NA), a CV beam produces a strong longitudinal electric or magnetic field component in the vicinity of the focal point that can be much stronger and have a much smaller cross-section than that of the transverse component. This specific property makes it possible to control the longitudinal component in addition to the transversal components, and expands the degree of freedom for designing electromagnetic-field distributions near the focal point. Some specific features of CV beams, which cannot be realized with Gaussian beams, have been reported, including, tighter focusing [2, 3], ultra-long depth focusing [4, 5], and specific in-plane electromagnetic field distribution at the focal point [6]. These unique properties have led to the application of CV beams in high-resolution imaging [7], optical trapping [8], efficient surface plasmon excitation [9], and so on.
As in the optical region, although to date only a limited number of systems allow the generation of terahertz (THz) CV beams, the generation and use of CV beams should have a significant impact on the evolution of research in the THz frequency region. First is the efficient coupling of a THz CV beam to a metal waveguide. Metal wires are promising candidates as THz waveguides that exhibit low loss and small dispersion [10]. However, the coupling efficiency of linearly polarized THz beams to cylindrical metal wires by a scattering process is less than 1% [11] due to the large mode mismatch between the surface plasmon modes of a metal waveguide and a free-space linearly polarized wave. To match the guiding mode and thereby enhance dramatically the coupling efficiency, radially polarized THz beams are highly desirable [11]. The second potential application is in the improvement of the resolution of THz imaging. THz imaging is one of the most important applications of THz technology [12, 13], and improvement of the spatial resolution is a critical issue, because the wavelength of a THz wave is as long as several hundred microns. A more tightly focused THz beam should contribute to an increase in the spatial resolution of THz imaging technology. Finally, the THz time-domain spectroscopy technique can realize the detection of the waveforms of electric field vectors of CV beams, including phase information. As a result, in the THz region, it is possible to directly observe the longitudinal electric field components and obtain specific phase information, such as the Gouy phase shift [14] of THz CV beams. Such information should contribute to the further understanding of the fundamental properties of CV beams, because direct observation of the longitudinal component in the optical region is difficult.
There are two types of fundamental CV modes: radial and azimuthal polarization modes. The electric field of the radial (azimuthal) mode in the transverse plane is aligned in the radial (azimuthal) direction. THz radial beam generation using photo-conductive antenna [11], plasma filamentation [15], and longitudinal polarization in nonlinear crystals [16] has been reported, and there are fewer reports of THz azimuth beam generation [17]. However, these methods require several improvements. In the case of the conventional photo-conductive antenna, the frequency of the radiated THz wave is limited in the low THz frequency regions, and it is difficult to increase the radiation intensity. With the nonlinear crystal based method described in Ref 16, the radiated THz frequency is also limited. When using filamentation, it is difficult to realize an ideal electric field distribution for the CV modes, and an intense pulse laser is required. Furthermore, a common problem of the previously reported methods is the difficulty to easily change between the radial and azimuthal THz CV modes.
In this study, we propose and demonstrate a simple method for THz CV beam generation using optical rectification in segmented nonlinear crystals with threefold rotational symmetry. We used segmented GaP(111) plates for the THz CV beam generation, and obtained clear evidence of the THz CV beam generation by the measurement using a THz camera. By this method, a broadband THz CV beam can be generated, and it is possible to easily switch between the radial and azimuth modes. We also report on the direct observation of the longitudinal electric field components at the focal point using a THz time-domain spectroscopy technique.
2. Experimental setup
If a nonlinear crystal has threefold rotational symmetry, linearly-polarized THz pulse is generated by linearly-polarized optical pulse excitation, and the amplitude of the radiated THz wave does not depend on the azimuthal angle ϕ of the linearly-polarized optical pulse. In this case, when ϕ changes by Δϕ, the azimuthal angle of the THz wave θ changes byΔθ = −2 Δϕ, as shown in Fig. 1(a) [18, 19]. Therefore, it is possible to change the polarization direction ofthe THz wave without changing the amplitude, by only changing the polarization direction of the fundamental beam.
Fig. 1 (a) Schematic picture of the THz radiation from a nonlinear crystal with threefold rotational symmetry. The red (green) arrow indicates the polarization of the fundamental (THz) beam. (b) Schematic picture of the segmented nonlinear crystals for THz CV beam generation. (c) Cutting design of the segmented pieces from a substrate. (d) A photograph of the segmented nonlinear crystals.
THz CV beam generation is realized by introducing a linearly-polarized optical pulse into nonlinear crystals in which the crystal axes vary spatially. The arrangement of a nonlinear crystal device for THz CV beam generation is schematically shown in Fig. 1(b). The device is composed of eight sectors of nonlinear crystals with threefold rotational symmetry, each one with a different orientation of the crystal axis. Such an approximate device was used because it is difficult to realize a nonlinear crystal in which the crystal axis varies continuously in space. In the optical region, a quasi-CV beam generation using an eight-segmented half-waveplate device was demonstrated, and the mode overlap between an ideal CV beam and such quasi-CV beam was evaluated as large as 93% [20]. It is enough for the demonstration as shown below. The direction of the crystal axes (11-2) are shown by the arrows in Fig. 1(b). Because of the relationship Δθ = −2 Δϕ, by rotating the crystal with an angle α around the (111) axis, the polarization of the THz pulse rotates with an angle of 3α. Therefore, in order to generate THz CV beams with polarization direction changes of 360° around the beam center in the transverse plane, the in-plane direction of the crystal axes (11-2) should vary completely by 120°, as shown in the left side of Fig. 1(b). In addition, because an additional 120° of in-plane rotation of the nonlinear crystals is allowed due to the threefold rotational symmetry, the relative angle of the crystal axes of neighboring crystals can be ψ = 120°/n + 120° (n: an integer), if the device is composed of n pieces of segmented nonlinear crystals. In this study, eight pieces of segmented nonlinear crystals were used, and ψ equals 135°, as shown in the right side of Fig. 1(b). The segmented nonlinear crystals were efficiently cut from a (111) substrate, as shown in Fig. 1(c).
An important feature of this method is that one can easily change the CV modes of the radiated THz beam simply by rotating the polarization direction of the fundamental beam by 45°, as shown in Fig. 2 . Moreover, the polarization direction of the radiated THz beam does not depend on the frequency. Therefore, the CV beam is realized over the entire frequency range of the THz radiation. In addition, by setting the relative angle of the crystal axes of neighboring crystal to 120° × m/n, higher-order THz CV beams with polarization direction changes of 360° × m around the beam center can be also generated.
Fig. 2 Relationship between the directions of polarization of the fundamental beam and the radiated CV modes
This method can be applied to any nonlinear crystals with threefold rotational symmetry. In this study, semi-insulating GaP(111) substrates with a thickness of 0.45 mm were used. Large GaP substrates can be obtained at a low cost and are suitable for broadband THz radiation, and have frequencies as high as 7 THz [21]. When the polarization direction of the fundamental beam is parallel to the (11-2) axis, the polarization direction of the radiated THz beam is the same as that of the fundamental beam [19]; therefore, the (11-2) axis is considered as the origin of θ and ϕ, as shown in Fig. 1(a). The eight triangle plates were cut from one GaP(111) substrate with a dicing saw, arranged on a polytetrafluoroethylene (PTFE) sheet without any adhesive, and fixed in place with a metal plate. The picture of the device is shown in Fig. 1(d).
In this study, we employed two measurement setups: one for the direct imaging of the electric field intensity distribution of the THz CV beams, and the other for the detection of the longitudinal electric field components at the focal point. The setup for the direct imaging of the electric field intensity distribution is shown in Fig. 3(a) . A regenerative amplified Ti:sapphire laser system (Legend Elite, Coherent, Inc.) with a 1 kHz repetition rate, a center wavelength of 800 nm, a pulse width of 25 fs, and a pulse energy of 2.7 mJ was used as the fundamental light source. The beam diameter in front of the segmented nonlinear crystals was 15 mm. For the detection of the THz CV beam, a THz camera (IRV-T0830, NEC Corp.) that enables real-time THz imaging was used. The camera consists of a 320 × 240 pixel uncooled micro-bolometer array with a 23.5 μm pixel pitch. In order to make the intensity of the THz CV beam high enough to be detected by the THz camera, a THz lens with a 30 mm focal length (Tsurupica, Pax Corp.) was placed in front of the THz camera that detected the image at the focal point of THz CV beam. A wire-grid polarizer (WGP) was placed in front of the THz lens in order to visualize the polarization state of the THz CV beam, and a PTFE sheet was inserted between the nonlinear crystals and the WGP in order to block the fundamental beam.
Fig. 3 Schematic structures of the experimental setups for (a) the direct imaging of the electric field intensity distribution of the THz CV beams, and (b) the detection of the longitudinal electric field components.
Figure 3(b) shows the experimental setup for the measurement of the electric field components at the focal point. The THz waveform was detected via THz time-domain spectroscopy using a scanning electro-optic (EO) sampling technique. A ZnTe(110) crystal was used for the detection of the transversal component. In this study, it was important to detect the longitudinal components; only the longitudinal electric field components could be detected by using the (100) plane of a nonlinear crystal with a Zinc Blende structure as the detection crystal [18]. Therefore, we selected a ZnTe(100) crystal for the detection of the longitudinal component. A regenerative amplified Ti:sapphire laser system (Hurricane, Spectra-Physic Lasers, Inc.) with a 1 kHz repetition rate, a center wavelength of 800 nm, a pulse width of 100 fs, and a pulse energy of 0.8 mJ was used as the fundamental light source. The direction of the segmented nonlinear crystals was set for the radial beam radiation, and a THz lens with a 30 mm focal length was also used for focusing the THz radial beam. The spatial distribution of the longitudinal and transversal electric field components was obtained by scanning the position of the probe beam near the focal point of the THz CV beams on the detection samples, which was achieved by changing the position of the iris placed inside the expanded probe beam, as shown in Fig. 3(b). The size of the iris image on the ZnTe crystal is about 0.4 mm. The probe beam scanned along the line across the center of the THz radial beam at the focal point.
3. Results
Figure 4 shows the intensity distribution images obtained for the THz radial (a–c) and azimuthal (d–f) CV beams with the WGP in the horizontal (a, d), 45° (b, e), and vertical (c, f) orientations at the focal point. For comparison, the images for a linearly polarized THz beam are also shown in Fig. 4(g–i). The in-plane polarization distribution of the radial (azimuthal) beams is also radial (azimuthal) at the focal point [22]. As expected for THz CV beams, two lobes are clearly observed in Fig. 4(a–f), and they are aligned along (perpendicular to) the polarization direction in the case of the radial (azimuthal) beam. These results clearly indicate that THz CV beams were successfully generated.
Fig. 4 The intensity distribution images obtained with a THz camera for the THz radial (a–c) and azimuthal (d–f) CV beams, and for a linearly polarized THz beam (g–i) with the WGP in the horizontal (a, d, g), 45° (b, e, h), and vertical (c, f, i) orientations.
Figure 5(a) and 5(b) shows the spatial dependence of the obtained time-domain THz waveforms of the transversal and longitudinal electric fields, respectively. In Fig. 5(a), it is clearly shown that the in-plane electric field vanishes at the center of the beam spot and the phase of the THz waves is opposite in the upper and lower sides compared to that of the center. Meanwhile, the strongest THz field is detected at the center of the beam spot in Fig. 5(b). These features are consistent with the properties of the transversal and longitudinal electric field components of a radial beam at the focal point [22].
Fig. 5 Spatial dependence of the obtained time-domain THz waveforms of (a) the transversal and (b) the longitudinal electric fields near the focal point.
If the detection crystal is slightly tilted in the EO sampling method, a transversal component is observed as a longitudinal component, and vice versa, resulting in some artifact signals. In the current case, the amplitude of the transversal component is expected much stronger than that of the longitudinal component; hence, it is important to exclude the ambiguity due to such artifacts. Based on the following three facts described below (the electric field distribution, the dependence on the polarization state of the incident beam, and the relative phase difference), we concluded that the signals shown in Fig. 5(b) are the longitudinal electric field components.
First, we examined the spatial distributions of the transversal and longitudinal components. Figure 6(a) and 6(b) show the spatial dependence of the experimental THz spectra of the transverse and longitudinal components as determined by Fourier transformation of the data in Fig. 5. Figure 6(c) and 6(d) show the calculation results for the field distribution of the radial beam near the focal point, which were obtained from the formulas described in Ref. 22. As we can see from the figures, the experimental and calculated results agree well although the experimental data are slightly broader along vertical axis than the calculation data due to the finite spot size of the probe beam. It indicates the validity of the method to discriminate the longitudinal and transversal components.
Fig. 6 Spatial dependence of the obtained time-domain THz spectra of (a) the transversal and (b) the longitudinal electric fields near the focal point. (c) and (d): respective corresponding calculated results.
Second, the dependence of the longitudinal electric field on the direction of the segmented nonlinear crystals was confirmed. As already mentioned, by only rotating the segmented nonlinear crystals by 45°, the THz CV mode is changed from the radial mode to the azimuthal mode. In addition, if the crystals are rotated by 90°, the mode remains the radial mode, but the sign of the electric field oscillation becomes the opposite. Therefore, it is expected that the longitudinal electric field component should vanish with a rotation of the crystals by 45°, and the oscillation sign of the longitudinal electric field component should become negative at a 90° rotation. Figure 7 shows the experimental data, and these results agree well with the expectations.
Fig. 7 Dependence of the longitudinal electric field waveforms on the direction of the segmented nonlinear crystals. (a) radial beam radiation setup; (b) rotated by 45°; and (c) rotated by 90°.
Third, the phase difference between the transverse electric field component Er(ρ) and the longitudinal component Ez(ρ) at the focal point were checked. The components are described in Ref. 22 as follows:
where ρ is the distance from the optical axis, γ is the angle that the ray makes with the axis, α is the maximum value of γ that corresponds to half of the aperture angle, k is the wavenumber and J0(x) and J1(x) are Bessel functions of the first kind. Equation (1) indicates that the phase difference between Er(ρ) and Ez(ρ) is π/2 independent of the frequency, because Er(ρ) is a real number and Ez(ρ) is a purely imaginary number. The THz waveforms and relative phase difference of the transverse and longitudinal electric field components are shown in Fig. 8(a) and 8(b), respectively. The experimentally observed phase difference between the transverse and longitudinal electric field components is almost π/2 over the entire frequency range of the THz radiation, and this result is consistent with Eq. (1).Fig. 8 (a) THz waveforms and (b) relative phase differences of the transverse and longitudinal electric field components.
All of these three experimental results described above, i.e., the electric field distribution, the dependence on the polarization state of the incident beam, and the relative phase differences, are consistent with the properties of longitudinal electric field components. Therefore, it is concluded that the waveform of the longitudinal electric field components is experimentally detected by focusing a THz radial beam.
One unique property of this method is the ability to easily switch between the radial and azimuthal modes, and also take the polarization state between them, by only changing the polarization direction of the excitation beam. Therefore, the ratio of the longitudinal and transversal components can be easily controlled. For example, a flat-top intensity distribution in a THz pulse with a high NA lens can be achieved by balancing the longitudinal component and the transverse component in the focal plane [6].
In this study, a THz lens with NA = 0.39 was used for focusing. In this case, at the focal plane, the peak amplitude of the longitudinal electric field is about 10% of that of the transversal electric field. If a THz lens with a larger NA is used, the contribution of the longitudinal electric field components at the focal point become dominant, and the specific features of the THz CV beam can be utilized for novel applications. For example, with a larger NA THz lens, the focus spot size of the THz CV beam will be smaller than that of a linearly polarized beam [3], i.e., tighter focusing is realized in the THz region. This technique can be applied to increase the spatial resolution of THz imaging. In addition, because light-matter interactions strongly depend on the polarization direction of light, selective excitation of dipole moment using non-propagating longitudinal electromagnetic field of THz CV beam should be realized. For example, ultrafast control of magnetic dipole moment has recently been attracting a lot of attention in the THz region [23], and ultrafast magnetization control of intense longitudinal magnetic THz field can extend the degree of freedom for controlling the direction of magnetization.
The peak amplitude of longitudinal electric field components observed in this study is approximately 30 V/cm. In order to increase the THz radiation power, using nonlinear crystals with larger nonlinear optical coefficients, such as ZnTe(111), is effective. If a 1030 nm laser source is used instead of an 800 nm laser, a thicker GaP plate can be used because the phase matching condition is satisfied [24], which is also promising for realizing broadband and intense THz CV beam generation.
6. Conclusion
We demonstrate a simple method for the generation of THz vector beams. We demonstrated THz CV beam generation using eight pieces of segmented nonlinear crystals with threefold rotational symmetry, in which the directions of the crystal axes were properly designed. We visualized the electric field intensity distribution of the THz CV beam using a THz camera, and confirmed that axial-symmetry polarization distribution was realized. We also demonstrated that the radiation mode was easily changed by simply rotating the segmented nonlinear crystals. Moreover, we directly observed waveforms of the longitudinal electric field components of the THz CV beam at the focal point. The suggested method can be used as a conventional technique for generating broadband THz CV beams, and it is beneficial for the development of THz applications.
Acknowledgments
We thank Ms. Suzuki and Mr. Sugawara of DISCO Corp. for dicing the nonlinear crystals. This research was supported by the Photon Frontier Network Program, KAKENHI (20104002), the Special Coordination Funds for Promoting Science and Technology of MEXT, Japan, and by the JSPS through its FIRST Program. NK and TH acknowledge supports by JSPS Research Fellowship.
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